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Homework Help: Decay of Upsilon(4S) into two B mesons in laboratory frame.

  1. Nov 22, 2011 #1
    1. The problem statement, all variables and given/known data
    B mesons can be created through the reaction chain e+e- → [itex]\Upsilon[/itex](4S) → B+B- by colliding beams of electrons and positrons head-on at centre-of-mass energy equivalent to the mass of the [itex]\Upsilon[/itex](4S) resonance.

    a) If the electron beam energy is 8GeV, show that a positron beam energy of 3.498GeV is required to produce a centre-of-mass energy equivalent to the mass of the [itex]\Upsilon[/itex](4S) resonance. Calculate the velocity β=v/c, and the Lorentz boost factor, γ, of the [itex]\Upsilon[/itex](4S) produced, in the laboratory frame.

    b) For case (a) whare are the maximum and minimum possible B meson momenta, as measured in the laboratory frame, resulting from the decay of the [itex]\Upsilon[/itex](4S)?

    2. The attempt at a solution

    a) ECM= M([itex]\Upsilon[/itex](4S)) = 10.5794 GeV
    s = (E1 + E2)2 - (p1+p2)2 (these momenta are vectors).

    Neglect the mass of electron and positron, so E= |p|
    E2 is unknown.

    Therefore, s = (8+x)2 - (8-x)2

    Work through to get x = 3.498 GeV as required.

    β=p/E = [itex]\frac{8-3.498}{8+3.498}[/itex] = 0.3915

    γ=1/(1-beta^2)^0.5 = 1.087

    Fairly confident my answers above are correct, just not sure how to go about part b at all. Any help is really appreaciated.

    Thoughts I had were to calculate the relativistic momentum and then use the cosine of the angle, the maximum value of cosine being 1 and the minimum being -1.
    Last edited: Nov 22, 2011
  2. jcsd
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